Many birds can easily fly over Everest.

There are buzzards which have reached 37,999 ft

Even the much misunderstood Canada goose is pretty impressive :

"The maximum flight ceiling of Canada geese is unknown, but they have been reported at 9 km (29,000 feet)."

These birds never encounters anything that high, but are capable of reaching astonishing heights.

Given temperature and O2 levels fall as altitude increases it is impressive that birds can even survive at those levels.

Bird lungs are impressively efficient.